Common merit rank is your All India Rank in that particular exam.

General merit rank is your category rank for general category student.

In
NIFT there is reservation for OBC, SC and ST. But if a person has 
applied for a reserved category then despite getting higher rank he/she 
can’t occupy the general seat. This goes for all the category. That’s 
why declaring general category rank (or any category rank) is important 
as there are specific seats reserved for all categories (including 
general).

You get your counselling call on 
the basis of your CMR (Except in case you’re PwD). Person with higher 
CMR of general category gets more preference for choosing the college of
his choice than the person with lower CMR of general category. Same 
goes with other categories too.